override object color on Linked Group
This is a common issue that will be resolved when overrides arrive in Blender.

However, a possible solution for your problem right now could be the following:
Drivers.

You can add drivers to the parameters in the node tree that you want to influence. E.g. attach the Factor of a Mix node to the x-Position of an Empty.
Make sure the Empty is in the same collection that you link.

Then, when you link the collection in a new blend file, you can create a proxy of the Empty and consequently use it to change the material.

I hope this helps point you to a working solution.